On some generalized numerical radius inequalities for Hilbert space operators
Volume 32, Issue 3, pp 257--262
http://dx.doi.org/10.22436/jmcs.032.03.06
Publication Date: September 29, 2023
Submission Date: June 25, 2022
Revision Date: August 09, 2023
Accteptance Date: August 25, 2023
Authors
F. Alrimawi
- Department of Basic Sciences, Al-Ahliyya Amman University, Amman, Jordan.
H. Kawariq
- Department of Mathematics, Faculty of Science, Philadelphia University, Jerash, Jordan.
Abstract
In this paper, it is shown, among other inequalities, that if \(A,B\in
\mathcal{\mathbb{B(H)}}\), then, for \(p\geq 1,\) we have%
\[
2^{\frac{1}{p}-2}\left\Vert \left\vert A^{\ast }\right\vert ^{2}+\left\vert
B\right\vert ^{2}\right\Vert _{p}\leq 2^{\frac{1}{p}-3}\left( \left\Vert
A^{\ast }+B\right\Vert _{2p}^{2}+\left\Vert A^{\ast }-B\right\Vert
_{2p}^{2}\right) \leq w_{2p}^{2}\left( \left[
\begin{array}{cc}
0 & A \\
B & 0%
\end{array}%
\right] \right)
\]
and%
\[
w_{2p}^{2}\left( \left[
\begin{array}{cc}
0 & A \\
B & 0%
\end{array}%
\right] \right) \leq 2^{\frac{1}{p}-1}\left( \left\Vert \left\vert
A\right\vert ^{2}\right\Vert _{p}+\left\Vert \left\vert B^{\ast }\right\vert
^{2}\right\Vert _{p}\right) -(2^{\frac{1}{p}-1}-1)\left\vert \left\Vert
\left\vert A\right\vert ^{2}\right\Vert _{p}-\left\Vert \left\vert B^{\ast
}\right\vert ^{2}\right\Vert _{p}\right\vert .
\]
Share and Cite
ISRP Style
F. Alrimawi, H. Kawariq, On some generalized numerical radius inequalities for Hilbert space operators, Journal of Mathematics and Computer Science, 32 (2024), no. 3, 257--262
AMA Style
Alrimawi F., Kawariq H., On some generalized numerical radius inequalities for Hilbert space operators. J Math Comput SCI-JM. (2024); 32(3):257--262
Chicago/Turabian Style
Alrimawi, F., Kawariq, H.. "On some generalized numerical radius inequalities for Hilbert space operators." Journal of Mathematics and Computer Science, 32, no. 3 (2024): 257--262
Keywords
- Numerical radius
- norm inequality
- Schatten \(p\)-norm
MSC
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